Most likely. It has to be submitted no earlier than five days before departure. One other thing with that form (although maybe they have fixed this now - for the names there is a "second surname" field which is meaningless to most of us from North America but is a required field because all Hondurans have at least four names as their legal name. I have always had to put "N/A" in that last field to get the form to go through without errors.
The risk of contracting dengue has reduced significantly since the state of emergency over dengue was declared (I think last July or thereabouts), even on the mainland. From what I understand the Bay Islands especially, being such a heavy tourist destination and the tax dollars resulting from the sales revenue to said tourists being very important to the government of Honduras, received more help than other parts of the country in combating the disease. For malaria - in twenty years I have never personally met anyone here that has contracted it (although I live at an altitude that the mosquito that transmits it doesn't like). As you indicated, these are mostly landlubber problems - on the Aggressor you are so far from shore most of the time that mosquitos are nowhere to be seen.
